Question 1 :
The vector $\displaystyle \vec{c}$ is perpendicular to the vectors $\vec{a}=(2,-3,1),\vec{b} = (1,-2,3)$ and satisfies the condition $\vec{c}$.$(\hat{i}+2\hat{j}-7\hat{k}) =10$. Then the vector $\hat{c}$ =
Question 2 :
Given $\vec{P} = 3\hat{i} - 4\hat{j}$ , Which of the following is perpendicular to $\vec{P}$?
Question 3 :
Find the area of the rectangle whose two sides are given by the vector $\vec{A} =(2\overset { \wedge }{ i } +\overset { \wedge }{ j } )\quad \vec{B} =(-2\overset { \wedge }{ i } +4\overset { \wedge }{ j) } $
Question 4 :
A vector $A$ is along the positive $z-$axis and its vector product with another vector $B$ is zero, then vector $B$ could be:
Question 5 :
The moment of the force, $\overrightarrow{F}=4\hat{i}+5\hat{j}-6\hat{k}$ at $(2, 0, -3)$, about the point $(2, -2, -2)$ is given by.
Question 6 : Which of the following operations between the two vectors can yield a vector perpendicular to either of them?<p></p>
Question 7 :
If the angle between two vectors is $ 60^o $, then $ \dfrac { \vec A.\vec B }{ |\vec A \times \vec B | } $ is
Question 8 :
Three vectors $\vec { A } =a\vec { i } +\vec { j } +\vec { k } ,\vec { B } =\vec { i } +b\vec { j } +\vec { k } ,\vec { C } =\vec { i } +\vec { j } +c\vec { k } $ are mutually perpendicular ($\vec { i } ,\vec { j } ,\vec { k } $ are unit vectors along $X,Y,Z$ axis respectively). The respective values of $a,b$ and $c$ are
Question 9 :
$\bar { A } -\bar { B }$ is parallel to each other ,and $\bar { C } $.Then which of the following us correct.($\lambda$ is positive constant)
Question 10 :
Given $\vec{A} = 2\hat{i} + p\hat{j} + q\hat{k}$ and $\vec{B}=5\hat{i}+7\hat{j} + 3\hat{k}$. If $\vec{A}|| \vec{B}$, then the values of $p$ and $q$ are, respectively,
Question 11 :
A force with components (-7, 4, 5) acts at the point (2, 4, -3). Find the magnitude of moment about the origin.<br>
Question 12 :
If $\vec{A}$ and $\vec{B}$ are perpendicular vectors and vector $\vec{A}=5\hat{i}+7\hat{j}-3\hat{k}$ and $\vec{B}=2\hat{i}+2\hat{j}-a\hat{k}$. The value of $a$ is
Question 13 :
At a given instant of time the position vector of a particle moving in a circle with a velocity $3\hat{i}-4\hat{j}+5\hat{k}$ is $\hat{i}+9\hat{j}-8\hat{k}$. lt's angular velocity at that time is<br>
Question 14 :
$\mathrm{A}$ and $\mathrm{B}$ are two perpendicular vectors given by $\vec{A}=5\hat{i}+10\hat{j}-3\hat{k}$ and $\vec{B}=2\hat{i}+4\hat{j}-c\hat{k}$. The value of $\mathrm{c}$ is:<br/>
Question 15 :
The magnitude of the X and Y components of $\vec{A}$ are 7 and 6. Also the magnitudes of the X andY components of $\vec{A}+\vec{B}$ are 11 and 9 respectively. The magnitude of $\vec{B}$ is:<br/>
Question 17 :
lf vectors $\vec{\mathrm{A}}$ and $\vec{\mathrm{B}}$ are given by $\vec{\mathrm{A}}=5\hat{\mathrm{i}}+6\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ and $\vec{\mathrm{B}}=6\hat{\mathrm{i}}-2\hat{\mathrm{j}}-6\hat{\mathrm{k}}$ then which of the following is/are correct?<br/>$a)\vec{\mathrm{A}}$ and $\vec{\mathrm{B}}$ are mutually perpendicular<br/>$\mathrm{b})$ Product of $\vec{\mathrm{A}}\times\vec{\mathrm{B}}$ is same as $\vec{\mathrm{B}}\times\vec{\mathrm{A}}$<br/>$\mathrm{c})$ The magnitude of $\vec{\mathrm{A}}$ and $\vec{\mathrm{B}}$ are equal<br/>$\mathrm{d})$ The magnitude of $\vec{\mathrm{A}}.\vec{\mathrm{B}}$ is zero<br/>
Question 18 :
The sum of the magnitudes of two forces acting at point is $18$ and the magnitude of their resultant is $12$. If the resultant is at $90^0$ with the force of smaller magnitude, what are the, magnitudes of forces
Question 19 :
The vector $\overline{P}=\mathrm{a}\hat{i}+\mathrm{a}\hat{j}+3\hat{k}$ and $\overline{\mathrm{Q}}=\mathrm{a}\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other. The positive value of 'a' is<br>
Question 20 :
The torque of force $\displaystyle \vec{F}= \left ( 2\hat{i}-3\hat{j}+4\hat{k} \right )$ N acting at the point $\displaystyle \vec{r}= \left ( 3\hat{i}+2\hat{j}+3\hat{k} \right )$ m about origin is (in N-m):
Question 22 :
If $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}| $ then angle between $\overrightarrow{a} $ and $\overrightarrow{b} $ is
Question 23 :
If $\vec{A}=3\hat{i}+\hat{j}+2\hat{k}$ and $\vec{B}=2\hat{i}-2\hat{j}+4\hat{k}$ then value of $|\vec{A}\times \vec{B}|$ will be
Question 24 :
Three vectors satisfy the relation $\displaystyle \vec{A}\bullet \vec{B}= 0\:and\:\vec{A}\bullet \vec{C}= 0,\:then\:\vec{A}$ is parallel to
Question 25 :
If $a$ , $b$ and $c$ are three non-zero vectors such that $a.|b \times c| = 0$ and $b$ and $c$ are not parallel then $a$ , $b$ and $c$ are
Question 26 :
If the vectors $\displaystyle \vec{P}= a\tilde{i}+a\hat{j}+3\hat{k}\:and\:\vec{Q}= a\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other then the positive value of a is
Question 28 :
Let $ \overrightarrow{A}=\hat{i}A \cos\theta +\hat{j} A \sin \theta $ be any vector. Another vector $\vec{B}$, which is normal to $A$ can be expressed as
Question 29 :
If force is $ \overrightarrow F = (60 \hat i + 15 \hat j - 3 \hat k) N $ and velocity $ \overrightarrow v = (2 \hat i - 4 \hat j + 5 \hat k) m/s $ , the instantaneous power is :-
Question 30 :
Assertion: The vectors $\displaystyle \vec{A}= 2\hat{i}-3\hat{j}+\hat{k}\:and\:\vec{B}= \hat{i}+\hat{j}+\hat{k}$ are mutually perpendicular.
Reason: $\displaystyle \vec{A}\bullet \vec{B}=0$
Question 31 :
Calculate the moment about the points C (1,1,1) of a force 5 N. acting along the line $\displaystyle \underset{AB}{\rightarrow}$ where A,B are the points (2,3,4),(3,5,6) respectively the distance being measured in m
Question 32 :
The position vectors of radius are $2\hat{i}+\hat{j}+\hat{k}$ and $2\hat{i}-3\hat{j}+\hat{k}$ while those of linear momentum are $2\hat{i}+3\hat{j}-\hat{k}$. Then the angular momentum is
Question 33 :
A particle moves in the $x-y$ plane under the action of a force $\vec { F }$ such that the value of its linear momentum $( \vec { P } )$ at anytime $t$ is $P _ { x } = 2 \cos t,$ $P _ { y } = 2 \sin t$.The angle $\theta$ between $\vec { F }$ and $\vec { P }$ at a given time $t$ will be
Question 34 :
Three vectors satisfy the relation $\displaystyle \overrightarrow { A } .\overrightarrow { B } =0$ and $\displaystyle \overrightarrow { A } .\overrightarrow { C } =0$, then $\displaystyle \overrightarrow { A } $ is parallel to:
Question 35 : <p>Let $\bar{A} =A \cos \theta \hat{i}+A \sin \theta \hat{j}$ be any vector. Another vector $\bar{B}$, which is normal to $\bar{A}$ can be expressed as</p>
Question 37 :
If $\vec{A}=2\hat{i}+3\hat{j}+\hat{k}$ and $\vec{B}=3\hat{i}+2\hat{j}+4\hat{k}$, then find the value of $(\vec{A}+\vec{B})\times (\vec{A}-\vec{B})$.
Question 38 :
The angles which the vector $\vec A =3\widehat{i}+6\widehat{j}+2\widehat{k}$ makes with the coordinate axes are
Question 39 :
If $\vec{A} \times \vec{B} = \vec{B} \times \vec{A}$, then the angle between $A$ and $B$ is
Question 40 :
If the scalar and vector products of two vector are $4\sqrt{3}$ and $144$ respectively, what is the angle between the two vectors?<br/>
Question 41 :
It is possible to have $ \underset{a}{\rightarrow}\times \underset{b}{\rightarrow}=\underset{a}{\rightarrow}.\underset{b}{\rightarrow} $ for some suitable seclection of $\underset{a}{\rightarrow} $ and $\underset{b}{\rightarrow} $ For example $\underset{a}{\rightarrow} $=$\underset{0}{\rightarrow} $ . The statement is
Question 42 :
Three forces $ \overrightarrow P $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are acting at a point in a plane. The angle between $ \overrightarrow P $ and $\overrightarrow Q $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are $ 150^{\circ} $ and $ 120^{\circ} $ respectively. Then for the equilibrium, forces $ \overrightarrow P $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are in the ratio :-
Question 43 :
If the resultant of two forces $P$ and $Q$ be equal in magnitude to one of the components $P$ and perpendicular to it in direction, then the value of $Q$ is <br/>
Question 44 :
Let a force $\displaystyle \vec{F}$ be acting on a body free to rotate about a point O and let $\displaystyle \vec{r}$ the position vector of any point P on the line of action of the force. Then torque $\displaystyle \vec{t}$ of this force about point O is defined as $\displaystyle \vec{t}= \vec{r}\times \vec{F}$<br>Given, $\displaystyle \vec{F}= \left ( 2\hat{i}+3\hat{j}-\hat{k} \right )N\:and\:\vec{r}= \left ( \hat{i}-\hat{j}+6\hat{k} \right )m$<br>Find the torque of this force.
Question 45 :
Vectors $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ make an angle $\displaystyle \theta =\frac{2\pi }{3}.$ If $\displaystyle \left | \vec{a} \right |=1, \left | \vec{b} \right |=2$ then $\displaystyle \left \{ \left ( \vec{a}+3\vec{b}\right )\times \left ( 3\vec{a}-\vec{b} \right ) \right \}^{2}=$
Question 46 :
The maximum magnitude of cross product of two vectors is $12$ units and the maximum magnitude of their resultant in $7$ units, then their minimum resultant vector will be a:
Question 47 :
Given $|\vec{A}_{1}| = 2$, $|\vec{A}_{2}|= 3$ and $|\vec{A}_{1} + \vec{A}_{2}| = 3$. Find the value of $(\vec{A}_{1} + 2\vec{A}_{2})\cdot(3\vec{A}_{1} -4\vec{A}_{2})$.
